It is known that the earliest waveform generating device employed a crystal oscillator as the waveform generating device for the system clock, and this included a programmable frequency divider, counter, multiplexer, controller and digital-to-analog convertor (D/A), as well as various devices and methods for generating a waveform by phase accumulation. The common disadvantage of the prior art is that the manufacturing cost is too high or the relative accuracy is not good enough. Although currently some devices for generating cycled waveforms of nonsingle period are available, which can provide various waveforms of different periods by using a system clock of low frequency, such conventional devices for generating cycled waveforms of nonsingle period employ of actual value filling, i.e. DC signal and AC signal are operated and processed in advance and then filled into said table. The disadvantage of such a method is that the output signal in said table will have no symmetry. Since a symmetrical and periodic signal such as a sine wave will be symmetrical with respect to a DC level, it is not necessary that the value in each cycled period for counting be filled into said table, so that the repeated parts can be deleted to reduce the size of said table. If the output signal is not symmetrical, such an advantage can not be achieved, and also because the DC portion is contained in the output value of said table, it is more troublesome in processing.